Hair particles causing cycles render to hang on 2.9
After some experimenting it seems I was wrong about the memory. I've learned that having too many particles definitely affects memory and render times.
To combat this I reduced the number of children by half which made a huge difference but then the hair looked too thin, so to compensate I thickened up the roots.
It seems that my system will alert me if blender is out of memory when using too complex meshes but not with hair particles. Also my render times have decreased significantly.